Hollows under the eyes can be improved with fillers
Some patients have volume loss while others also can have fat pad or muscular protrusion along with volume loss. Check with an expert Dermatologic Surgeon to see if you are a candidate for the fillers or if you need other procedures to improve the under eye appearance.
Tear Troughs and injections
It is very difficult to see from the photo but it appears that you might need a traditional blepharoplasty to remove the fat pads under your eyes. These fat pads are usually genetic and run in families. Does your Mom have similar "tired-looking" eyes? Please find a board certified physician who has a great deal in cosmetics for the best results.
Can I fill these teartroughs or will it look worse?
Its best you schedule an in-person consult to get fully evaluated, there are many different options to help eliminate the tear troughs
Filler in the Tear Trough Region
It is difficult to tell from the photograph if you would benefit from fillers in the tear trough region. Some products do produce more swelling than others. Without examining you in person I am not able to give you more information. It may be worth getting another opinion from an experienced injector.
Teazerbee, I cannot tell a thing from your photo. I would recommend you see 2-3 facial plastic specialists and get more opinions. Frequently for this problem in my office I'm doing a "SOOF lift blepharoplasty". See my web site for further information. Good luck!!